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Tactile-based Object Center of Mass Exploration and Discrimination

Kunpeng Yao, Mohsen Kaboli*, and Gordon Cheng

Abstract— In robotic tasks, object recognition and discrim-

ination can be realized according to their physical properties,

such as color, shape, stiffness, and surface textures. However,

these external properties may fail if they are similar or even

identical. In this case, internal properties of the objects can be

considered, for example, the center of mass. Center of mass is an

important inherent physical property of objects; however, due

to the difﬁculties in its determination, it has never been applied

in object discrimination tasks. In this work, we present a tactile-

based approach to explore the center of mass of rigid objects

and apply it in robotic object discrimination tasks. This work

comprises three aspects: (a) continuous estimation of the target

object’s geometric information, (b) exploration of the center

of mass, and (c) object discrimination based on the center of

mass features. Experimental results show that by following our

proposed approach, the center of mass of experimental objects

can be accurately estimated, and objects of identical external

properties but different mass distributions can be successfully

discriminated. Our approach is also robust against the textural

properties and stiffness of experimental objects.

I. INTRODUCTION AND RE LATED WO RK

Tactile object recognition are of great signiﬁcance in

robots’ interaction with the environment [1]. Objects can

usually be distinguished from their physical properties such

as shape, surface texture, and stiffness [2]–[6]. However,

if the target objects have the identical external physical

properties, the above-mentioned features can not be applied

for discrimination tasks. To declare if the target objects

are identical, the robot should also verify their internal

properties. Center of mass (CoM) is an important inherent

physical property of the objects. It reveals the object’s mass

distribution. In particular, CoM is a constant position with

respect to rigid objects. However, CoM has never been used

in robotic object recognition/discrimination tasks, due to the

complexity and difﬁculty in its determination.

A. Related Work

Several previous work has been done on the topic of

estimating the target object’s center of mass. One approach

is to estimate the CoM of the target object via robotic

manipulation tasks. Atkeson et al. [7], [8] estimated the CoM

of the load of a robotic arm during a manipulation task. The

CoM position is formulated as a parameter of this robotic-

load system and estimated by solving the dynamic equa-

tion during manipulation. However, this approach requires

accurate models and parameters of the robotic system, and

Kunpeng Yao, Mohsen Kaboli, and Gordon Cheng are with the Institute

for Cognitive Systems, Department of Electrical and Computer Engineering,

Technical University of Munich, Germany. * Mohsen Kaboli is the cor-

responding author. Email: mohsen.kaboli@tum.de. Video to this

paper: http://web.ics.ei.tum.de/˜mohsen/videos/Humanoids2017.mp4

UR10 Robot

Robotiq Gripper

Finger A

Finger C

Finger B

SCF

ZS

YS

XS

OptoForce 3-Axis

Force Sensor

(OMD-20-SE-40N)

OCF

YO

ZO

XO

WCF

XW

YW

ZW

Fig. 1: System description: the UR10 robotic arm, the

Robotiq gripper, and the OptoForce 3D Force sensors.

the experimental result was inaccurate due to the unmodeled

dynamics. This approach also suffers from the inﬂuence of

the gravitational torque. Another approach estimate the CoM

by executing tipping actions on the object. In [9]–[11], the

CoM of the target object is obtained by determining the

“gravity equi-effect planes” or the “passing-C.M lines”. The

robotic arm installed with force sensors tips the object using

its ﬁngertip. The planes or lines that pass through the CoM

can be calculated based on the ﬁnger position and force

information recorded during the tipping movement. However,

this approach requires the estimation of the ﬁngertip vector

and the accurate representation of lines and planes, which

are of high computational complexity. The precise shape,

position, orientation of the target object is already given as

prior knowledge. In addition, the target object must maintain

a stable contact on the table surface without any slip while

it is being tilted by the ﬁngertip. In this work, we propose

a purely tactile-based approach to determine the CoM of

target object, which is model-free and of low computational

complexity, thus can be applied in on-line robotic tasks.

B. Contribution

We propose a tactile-based approach to explore the CoM

of rigid object in an unknown workspace and apply the CoM

feature in robotic object discrimination task.

•We ﬁrst propose a strategy to continuously estimate the

geometric information of regular shaped target objects

in an unknown workspace.

•Then, we present a tactile-based approach to explore

the CoM of rigid objects by applying lifting actions in

a three-sensing-point case.

•Furthermore, we formulate the CoM information as a

constant physical feature of the object, which can be

applied in object discrimination or identiﬁcation tasks.

II. SYS TEM DESCRIPTION

The robotic system (see Fig. 1) is composed of a 6-DoF

UR10 (Universal Robots) robotic arm, a RobotiQ 3-ﬁnger

industrial gripper, and an OptoForce sensor set.

The gripper has three ﬁngers, denoted as A, B, and C.

The OptoForce OMD-20-SE-40N 3D tactile sensor set has

four sensor nodes, each one can measure 3D forces on its

surface. A corresponding Sensor Coordinate Frame (SCF) is

deﬁned for each sensor node on the vertex of its external

semi-sphere surface1(see Fig. 1). Three sensor nodes were

installed on each ﬁngertip of the gripper. The sensing point

of each ﬁnger (i.e. ﬁngertip installed with tactile sensor node)

are denoted as P

A,P

B, and P

C, respectively; P

Band P

Care on

the same side and symmetric with respect to P

A. The World

Coordinate Frame (WCF) is a Cartesian coordinate system

located at the origin of the workspace. The table surface is

set as the reference plane. The workspace is a cuboid volume

above the reference plane: [xW,xW]×[yW,yW]×[zW,zW], and

spacial position located inside is denoted as (xW,yW,zW).

We use normal force f n

ito denote the amplitude of the

force component in Z+

Sdirection, which is also referred to as

the grasping force. The tangential force can be decomposed

into two components: the one along Z+

Waxis is named lifting

force, and denoted as fl

i, while the other component is

neglected, since it does not inﬂuence the analysis.

III. METHODOLOGY

We ﬁrst introduce the estimation of geometric information

of target objects in Sec. III-A; the tactile-based criterion for

CoM and the CoM exploration strategy are analyzed from

Sec. III-B to Sec. III-C, followed by the extraction of CoM

feature in Sec. III-D.

A. Tactile-based Object Geometric Information Estimation

We explain how to continuously explore the shape of a

quadrilaterally-faced hexahedron object in order to estimate

its geometric information, which is required for the CoM

exploration.

Tactile information detected on the sensor node is used as

feedback to control the movement of the robot. Two kinds

of points are of interest during exploration: contact point,

which is detected when the exploratory sensor touches the

object surface, i.e. as soon as the resultant force measured on

the exploratory sensor has exceeded a pre-determined small

value (|fA|>¯

fε); and separate point, which is detected when

the exploratory sensor detaches from the contacted object,

i.e. as soon as the temporal resultant force detected by the

exploratory sensor reduces below a threshold (|fA|<fε).

The proposed approach can be applied to quadrilaterally-

faced hexahedron objects, whose faces are quadrilaterals.

Each face can be deﬁned by detecting three non-collinear

contact points on it. Then explore the contacted face by

moving from contact points on the plane towards different

directions, the robot can collect separate points on edges of

1The subscript “S”, “W”, and “O” denote the SCF, WCF, and OCF (object

coordinate frame) coordinate frame, respectively; “+” and “-” denotes the

positive and negative direction of the corresponding axis.

Xw

Yw

Zw

PS1

PS2

Starting Plane

Tar ge t Plane

Exploratory

Direction

PC1

PC2

PE1

PE2

PE3

Main Axis

Estimated Centroid

✓

Fig. 2: The continuous exploration of a cuboidal experimen-

tal object in an unknown workspace.

the face, whereas each edge is determined by two separate

points. As soon as all of the edges are known, the vertices of

this side face are obtained; and the geometric information,

such as location, orientation, and shape, can be estimated

based on all the vertices of this target object.

Here we take a cuboidal object as example (see Fig. 2),

and explain the continuous exploration process in detail. To

increase the available exploration space, only one ﬁnger is

stretched out, which is referred to as the exploratory ﬁnger,

while the other two ﬁngers are curled up. The sensor node

installed on the ﬁngertip of exploratory ﬁnger is referred

to as the exploratory sensor. Without loss of generality,

deﬁned the X−

Waxis as the exploratory direction, and the

plane perpendicular to it, i.e. XW-YW-ZW, as the starting plane

(all points on this plane satisfy x=xW), while XW-YW-ZW

as the target plane (x=xW). The gripper ﬁrst stretches out

the exploratory ﬁnger (e.g. ﬁnger A), moves the exploratory

sensor to a starting position P

S1on the starting plane, and

adjusts the orientation of the exploratory sensor towards

X−

Wdirection. Then the robot pushes the exploratory sensor

towards the exploratory direction and tries to detect contact

with the target object. If a contact point is detected, the

current WCF coordinate of the exploratory sensor is recorded

as the ﬁrst contact point P

C1, and the robot immediately

stops its current movement. However, if no contact point

is detected until the sensor node has moved to the target

plane, the robot will retreat back, select another starting

position, and repeat this exploration, until a contact point is

detected. Since side faces of a cuboid are perpendicular to the

reference plane, under this condition, only two contact points

on the same side face are sufﬁcient for representing this

plane. Starting from P

C1, the robot ﬁnger continues to slide2

the exploratory sensor node upwards until a separate point

P

E1is detected, indicating the detection of an edge of object.

Then, the robot retreats the exploratory sensor back to the

starting position P

S1. The robot then chooses another starting

2Slide means that the exploratory sensor node is pressed to maintain a

non-zero contact force on the face of the target object during the entire

movement.

position P

S2, which is selected by horizontally moving a

distance from P

S1on the starting plane. Starting from P

S2, the

robot repeats the same movement towards the X−

Wdirection

and tries to detect another contact point P

C2. Set the line

←−−→

P

C1P

C2as the trajectory of the exploratory sensor, the robot

slides the exploratory sensor node starting from P

C1and P

C2

to obtain another two separate points P

E2and P

E3on two

vertical edges of this side face. Using these collected points

(two contact points to determine the plane, and three separate

points to determine three edges respectively), this side face

can be fully reconstructed, and all of its four vertices are

obtained. After this, the robot moves to the other side of

the workspace and starts exploration in the X+

Wdirection to

obtain the four vertices of the opposite side face, following

the same process as described above. The entire process of

geometric information estimation is completed as soon as

all of the vertices are obtained. Represent the set of vertices

as {Vi},i∈1,2,...,N(N=8 for hexahedrons), and the

coordinate of Viis (Vx

i,Vy

i,Vz

i). The centroid of the object O

is calculated as O= (xo,yo,zo) = 1

N∑iVx

i,∑iVy

i,∑iVz

i,i=

1,2,...,N. Since the object lies on the reference plane XW-

OW-YW, its location in the workspace is the projection of its

centroid on this plane, i.e. (xo,yo). We deﬁne the main axis l ∗

of the target object as the line that passes through its centroid

and is parallel to the reference plane, and along which the

object has the largest length. The orientation of the object

is represented as the included angle θ,θ∈[−π/2,π/2],

between its main axis and the X+

Waxis.

The robot rotates the gripper according to θ, such that

the line passes through two sensing points (P

Band P

C)

is parallel to l∗. For cuboid, its length, width, and height

can be easily obtained by directly calculating the distances

between adjacent vertices. The origin of its OCF can locate

at one arbitrary vertex, and the axes XO,YO, and ZOare

deﬁned along its length edge, width edge, and height edge,

respectively.

B. Center of Mass Determination

We propose to determine the CoM of the target rigid object

by applying lifting action. Consider the process of lifting

a steelyard balance as an example. It can be lifted up and

maintain balance without rotation if and only if the lifting

force passes through its CoM.

Represent the CoM in OCF of the target object as C=

(cx,cy,cz). Each component can be determined by searching

for one point of application for the lifting force along the

corresponding axis in OCF; through this point of application,

the object can be lifted up while maintaining equilibrium

state. We take the determination of cxas an example. In this

work, we discuss the three-sensing-point case (each contact

point can sense the force signals), satisfying that (1) two

sensing points (e.g. P

Band P

C) are aligned on the one side of

the grasped object, and (2) their positions are symmetric with

respect to the other sensing point (e.g. P

A) on the opposite

side of the object. This condition can be satisﬁed here by

controlling the gripper in pinch mode. While applying lifting

action to the target object, the gripper grasps the object at one

lifting position and lifts it up for a small distance ∆h. At the

equilibrium, both force condition and torque condition are

satisﬁed, which state that both resultant force and resultant

torque applied on the object are zero. We show that during

lifting, the force condition can be checked via linear slip

detection, whereas the torque condition can be veriﬁed by

detecting the rotation of the target object.

1) Force Condition Veriﬁcation via Linear Slip Detection:

According to the Coulomb’s law of friction, the largest value

of ﬁction that the gripper can provide is µ·fN, where µis

the friction coefﬁcient on the contact plane and is considered

as a constant value. If the grasping force applied by the

gripper is insufﬁcient, the resultant lifting force F=∑fl

iis

not able to balance the gravity, and linear slip happens on the

grasping point, i.e. F<G−FN,Gis the weight of the object

and FNis the supporting force from the table (if exists).

Force condition is sufﬁcient but not necessary for equilibrium

state, it can be satisﬁed by regulating the grasping force. The

force regulation is realized by linear slip detection on each

one of the contact points. We detected linear slip signals

by measuring the changing rate of tangential force on the

contact surface [12].

If slip signal is detected on anyone of the contact points,

the applied grasping force is considered insufﬁcient. Then

the gripper increases its grasping force by further closing its

ﬁngers and tries to lift the object again. The robot repeats this

procedure until the target object can be lifted up to the target

height without linear slip, indicating the satisfaction of force

condition. The next step is to check the torque condition.

2) Torque Condition Veriﬁcation via Rotation Detection:

Torque is hard to measure without torque sensors’ feedback.

Non-zero resultant torque applied on the object causes ro-

tation of the object with respect to the contact point, hence

we verify the torque condition by detecting the rotation of

the target object during lifting process. Due to the positional

symmetry, the tangential forces on P

Band P

Cshould be equal

during the entire lifting process, if and only if the object

is in equilibrium, i.e. tangential force applied on P

Apasses

through the CoM. Represent the sequence of force signals

that recorded continuously on contact point iduring lifting

process as fi,i∈A,B,C. According to the analysis above, if

fBis highly similar to fC, it can be concluded that the current

lifting position is close to the real CoM of the object.

We propose to use the cross-correlation to measure the

similarity of force signal sequences due to its robustness

and sensitiveness. Cross-correlation measures the correlation

between two jointly stationary series and has a normalized

measurement in the range of [−1,1](see Fig. 3). The cross-

correlation criterion for checking the torque condition can be

formulated as:

ρBC =cov(fB,fC)

σfBσfC

≥δ,ρBC ∈[−1,1],δ∈(0,1)(1)

with cov(fB,fC)being the cross-covariance of fBand fC,

whereas σfBand σfCthe standard deviation of fBand fC,

respectively. The closer ρBC to 1, the higher the similarity

between fBand fC. This criterion is independent of the

5 10 15 20 25 30 35 40

Position of Lifting

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Cross Correlation

Cross-Correlation ;BC

(a) ρBC

5 10 15 20 25 30 35 40

Position of Lifting

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Cross Correlation

Cross-Correlation ;AB and ;AC

;AB

;AC

(b) ρAB and ρAC

Fig. 3: The cross-correlations (Y axis) at different lifting

positions (X axis) along the XOaxis of an experimental

object. At each position, the robot stably lifted the object

to ∆h=30mm. Lifting forces on each contact point are

recorded during lifting for analysis.

absolute force values and thus can be applied on objects

of different shapes, textures, and stiffness.

To determine if a lifting position can be estimated as CoM,

the robot ﬁrst tries to lift the object at this position and

regulates its grasping force via linear slip detection. Once

the force condition is satisﬁed, the robot evaluates ρBC for

the torque condition. If ρBC is close to 1, the current lifting

position is considered close to the CoM.

C. Center of Mass Exploration

Now we explain how to search for the CoM of a regular

shaped rigid object along one dimension. The geometric

information estimated in Sec. III-A is required. In the fol-

lowing, we take the exploration of cx(in the XO-axis) as an

example. At the target lifting position, both force condition

and torque condition can be satisﬁed. The binary search

algorithm of the computational complexity O(log2N)(for

Npossible sampling points) is the optimal candidate for this

one-dimensional search problem, and tactile feedback is used

to guide the search.

In this three-sensing-point case, we show that between the

two contact points on the same side (e.g. P

Band P

C), the one

that is closer to the real CoM of the target object senses larger

linear friction force than the other while the object is lifted

up by these three contact points.

Since the lifted object does not move horizontally, normal

forces satisfy fn

1=fn

2+fn

3; and due to the symmetry of P

B

and P

C,fn

2=fn

3,fn. Assume the object does not rotate

with respect to the main axis, thus it holds that fl

1=fl

2+fl

3

according to the torque condition. Represent the ratio of fl

to fnfor contact points 2 and 3 as αand β, respectively.

Since force condition is satisﬁed, no linear slip happens on

the contact surface:

fl

2=αfn

2≤µfn

2=µfn,(2)

fl

3=βfn

3≤µfn

3=µfn.(3)

Forces in ZWaxis balance and meet fl

2+fl

3= (mg −fN)/2,

where fNis the supporting force from the reference plane

(fN=0 if the object is not supported by the table). Select the

reference point on the main axis, and the distances between

each lifting force vector to the reference point are denoted

as ri,i=1,2,3; rgdenotes the distance from the weight

vector mgto the reference point. According to the torque

condition, r1fl

1+r2fl

2+r3fl

3=mgrgwith mbeing the mass

of the object and gthe gravitational acceleration.

Reformulating the above equations result in:

α+β= (mg −fN)/(2fn)>0,(4)

(r1+r2)α+ (r1+r3)β=mgrg/fn,(5)

and thus the following relationship holds:

α+β= ((r1+r2)α+ (r1+r3)β)/C,(6)

C=2mgrg

mg −fN

>0.(7)

Without loss of generality, we assume r3>r2. Since (α+

β)fnrepresents the minimal resultant lifting force to main-

tain force condition in ZWdirection, for a given fn,α+β

has the minimal possible value. If α>0,β>0, according

to Eq. 6, α+βreaches its minimum value if and only

if α/β= (r1+r3)/(r1+r2). Then α>βand fl

2>fl

3. If

α·β<0, then α>0>βand |α|>|β|, and fl

2>fl

3is also

satisﬁed. Fig. 3(b) shows an experimental veriﬁcation of this

conclusion. This conclusion is used to determine the next

lifting position. We use the cross-correlation ρAB and ρAC to

evaluate the similarity of signal sequences. The next lifting

position lies in the range that is closer to the contact point

that senses larger tangential force. For example, if ρAB >ρAC ,

the next lifting position should be closer to P

Bwhile further

to P

C.

In each exploration step, the robot bisects the remaining

search region and chooses the middle point as the next lifting

position, until has found one lifting position that can be

estimated as the CoM.

D. CoM Feature Extraction

The CoM feature is deﬁned with respect to the OCF.

Along each dimension of the OCF, the edge of the object

is segmented by the CoM component into two parts. We

use the superscript “ +” to denote the longer segment and

“−” the shorter segment. Then in each dimension, the CoM

feature is deﬁned as the ratio of these two parts.

λ

λ

λ= (λx,λy,λz) = x−

O/x+

O,y−

O/y+

O,z−

O/z+

O.(8)

Each component of λ

λ

λis normalized in (0,1]. As long as the

OCF is determined, the CoM feature can be extracted as a

constant vector.

IV. EXP ERI MEN TAL EVA LUATI ON

We designed two scenarios to experimentally evaluate

the performance of our proposed approaches. In the ﬁrst

scenario, the robot estimated target object’s geometric infor-

mation and then explored its CoM. Experimental objects of

distinct textures, stiffness, and sizes were used. In the second

scenario, the robot tried to discriminate several experimental

objects according to their CoM features.

Object 1 Object 2 Object 3

S: + T: ++ C: +S: ++ T: -- C: +S: + T: -- C: +

Object 4

S: ++ T: -- C: +

Object 5 Object 6

S: ++ T: ++ C: + S: + T: - C: ++

Object 9 Object 10 Object 11

S: - T: + C: +

Object 12

S: - T: ++ C: 0 S: - T: + C: ++ S: -- T: ++ C: +

S: -- T: -- C: 0 S: - T: - C: ++

Object 7 Object 8

Fig. 4: Experimental objects. ‘S’: stiffness, from very soft (-

-) to very hard (++). ‘T’: textural properties, ranging from

very ﬁne (- -) to very rough (++). ‘C’: distance between CoM

and geometric center, ‘0’ means CoM coincides geometric

center, while ‘++’ indicates CoM is far from geometric

center.

(I) (II) (III)

Fig. 5: For multiple objects, the entire workspace is seg-

mented into different regions, i.e. (I), (II), and (III), and the

robot explores target object located in each region.

In this work, we used cuboidal objects and only consider

the 1D CoM feature λx(i.e. the length edge of the object),

due to the hardware constraints, which mainly come from

the shape of the gripper. In addition, neither location nor

orientation of the target object is supposed to change after

the geometric information estimation. Therefore, to maintain

the stability of the target object during CoM exploration,

cylinder-shaped objects or objects with curved surfaces are

not taken into consideration.

A. CoM Exploration of Single Experimental Object

In this scenario, the task of the robot is to explore the

CoM of several experimental objects, which have different

physical properties, such as shape, textures, stiffness, and

CoM locations. Due to the hardware constraint, it is difﬁcult

to estimate the geometric information of all the target objects

simultaneously. For multiple target objects (see Fig. 5), the

entire workspace is segmented into several regions, and the

robot explores each one of the target objects located in the

corresponding region successively.

Here we take the object in the region (II) as an example.

Fig. 6 shows the reconstructed object after the geometric

information estimation (see Fig. 2). The size of Object 1 was

estimated as 40.2mm ×3.6mm ×5.8mm, while the measured

real size is 40.0mm ×3.8mm ×6.0mm.

Then the robot adjusted the orientation of the gripper and

started to explore the CoM along the XOaxis (see Fig. 8). At

each lifting position, the object was lifted up to ∆h=30mm

above the reference plane. The CoM exploration terminates

as soon as either the next search range is smaller than 10mm

Fig. 6: The reconstructed shape of the target object.

TABLE I: Explored CoM Features of Experimental Objects

Object Nr. 1 2 3 4 5 6

λx0.784 0.865 0.897 0.579 0.600 0.428

Object Nr. 7 8 9 10 11 12

λx0.998 0.291 0.833 0.909 0.218 0.769

or ρBC >δ=0.9. The CoM component was estimated as

λx=0.681 within six steps, with an error range of L×2−6=

6.25mm (L=40.0mm).

The estimated CoM components λxof each experimental

object are listed in Table I.

Object 1 Object 2 Object 3

S: + T: -- C: 0 S: + T: -- C: + S: + T: -- C: ++

Fig. 7: We deliberately manufactured three experimental

objects, which have identical stiffness, surface textures, and

sizes, while distinct CoMs (marked by the red region).

B. CoM-based Object Discrimination

Three manufactured objects (see Fig. 7) are used in

this scenario (see Fig. 1). They have the identical physical

properties, while their CoMs are modiﬁed to be distinct by

deliberately adjusting their inner structures.

The robot collected the CoM feature of each object for

20 trials. The mean values of the explored λxof each

experimental object are listed in Table II. This 1D dataset

was clustered by segmenting the estimated kernel density at

its local minimum values. We used Gaussian kernel with a

bandwidth of 0.025 for the KDE (Kernel Density Estimation)

analysis. Result shows that the sampled CoM featured can

be clustered into three classes, with an adjusted rand index

of 1.0, indicating that all the collected CoM features are

successfully clustered (see Fig. 9).

TABLE II: Explored CoM Features in Sec. IV-B

Object Nr. 1 2 3

λx0.927 0.784 0.346

(A-1) (B-1) (C-1) (D-1) (E-1) (F-1)

A

B C

Explored CoM

2 4 ×103 2 4 ×103 2 4 ×103 2 4 ×103 2 4 ×103 2 4 ×103

(A-2) (B-2) (C-2) (D-2) (E-2) (F-2)

Real CoM

Lifting Position

Fig. 8: The process of exploring the CoM of a regular shaped rigid object using binary search approach based on tactile

feedback. In each column, the upper subﬁgures (A-1) - (F-1) show the lifting position at each sample step. The real CoM

of this target object is marked by the red region, and the yellow triangle in each ﬁgure indicates the current lifting position.

The lower subﬁgures (A-2) - (F-2) show the corresponding sensor signal sequences of each ﬁnger recorded during lifting.

Fig. 9: Clustering result of CoM features based on KDE.

V. C ONCLUSION AND FUTURE WORK

In this paper, we proposed a tactile-based approach to

explore the CoM of rigid objects in an unknown workspace

for robotic object discrimination tasks. We ﬁrst presented a

continuous exploration approach for the robot to estimate

target object’s geometric information, which can be applied

to quadrilaterally-faced hexahedron objects. Then, we ana-

lyzed the conditions that the applied force and torque should

satisfy when the object is lifted up at its CoM, and proposed

the strategy to explore the CoM of a target rigid object. It

is worth mentioning that the applicability of the proposed

CoM exploration approach is independent of the number

of grasping ﬁngers, rather only depends on the sensing

points. Furthermore, we formulated the CoM information as

a constant feature deﬁned in the OCF, which is insusceptible

to the external properties of the object and can be applied in

object discrimination and recognition tasks.

The scope of this work is focused on the regular shaped

rigid objects. In the future, we plan to generalize our

approach for irregular shaped objects or soft objects by

removing the constraints from hardware, i.e. using dexterous

robotic hand and multi-modal tactile sensors. In our proposed

method, at least three sensing points are required to detect

the rotation of lifted object. The number of sensing points

can be further reduced if the occurrence and direction of

rotational slip can be detected. In addition, it is possible to

accelerate the exploration process of the CoM for a novel

object by taking advantage of the prior knowledge, i.e. by

transferring the mass distribution information of the explored

objects to a novel target object.

ACKNOWLEDGMENT

Many thanks to OptoForce Ltd. for providing tactile

sensors for this study.

REFERENCES

[1] R. S. Dahiya, G. Metta, M. Valle, and G. Sandini, “Tactile sensing—

from humans to humanoids,” IEEE Transaction on Robotic, vol. 26,

no. 1, pp. 1–20, 2010.

[2] M. Kaboli, P. Mittendorfer, V. Hugel, and G. Cheng, “Humanoids

learn object properties from robust tactile feature descriptors via multi-

modal artiﬁcial skin,” IEEE Int. Conf. on Humanoid Robots, 2014.

[3] M. Kaboli, R. Walker, and G. Cheng, “In-hand object recognition via

texture properties with robotic hands, artiﬁcial skin, and novel tactile

descriptors,” IEEE International Conference on Humanoid Robots,

pp. 2242–2247, 2015.

[4] M. Kaboli, R. Walker, and G. Cheng, “Re-using prior tactile expe-

rience by robotic hands to discriminate in-hand objects via texture

properties,” IEEE International Conference on Robotics and Automa-

tion, pp. 2242–2247, 2016.

[5] M. Kaboli, D. Feng, K. Yao, P. Lanillos, and G. Cheng, “A tactile-

based framework for active object learning and discrimination using

multimodal robotic skin,” IEEE Robotics and Automation Letters,

vol. 2, no. 4, pp. 2143–2150, 2017.

[6] M. Kaboli, D. Feng, and G. Cheng, “Active tactile transfer learning for

object discrimination in an unstructured environment using multimodal

robotic skin,” International Journal of Humanoid Robotics, 2017.

[7] C. G. Atkeson, C. H. An, and J. M. Hollerbach, “Rigid body load

identiﬁcation for manipulators,” IEEE Conference on Decision and

Control, pp. 996–1002, 1985.

[8] C. H. An, C. G. Atkeson, and J. M. Hollerbach, “Estimation of inertial

parameters of rigid body links of manipulators,” in IEEE Conference

on Decision and Control, vol. 24, pp. 990–995, 1985.

[9] Y. Yu, K. Fukuda, and S. Tsujio, “Estimation of mass and center of

mass of graspless and shape-unknown object,” in IEEE International

Conference on Robotics and Automation, vol. 4, pp. 2893–2898, 1999.

[10] Y. Yu, T. Kiyokawa, and S. Tsujio, “Estimation of mass and center

of mass of unknown and graspless cylinder-like object,” International

Journal of Information Acquisition, vol. 1, no. 01, pp. 47–55, 2004.

[11] Y. Yu, T. Arima, and S. Tsujio, “Estimation of object inertia parameters

on robot pushing operation,” in IEEE International Conference on

Robotics and Automation, pp. 1657–1662, 2005.

[12] M. Kaboli, K. Yao, and G. Cheng, “Tactile-based manipulation of

deformable objects with dynamic center of mass,” IEEE International

Conference on Humanoid Robots, pp. 790–799, 2016.